X and Y complete a task in 14 days, Y and Z in 18 days. X works 6 days, Y works 8 days, Z works 12 days to complete it. How many days for Z alone(approximate)?

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**Solution**

1. Let rates be $x,y,z$ tasks/day for X, Y, Z. Given $x+y=1/14$ and $y+z=1/18$.
2. Total work: $6x+8y+12z=1$.
3. Put $x=1/14-y$ into the work eq: $6(1/14-y)+8y+12z=1$ which gives $2y+12z=4/7$.
4. Put $y=1/18-z$ into that: $2(1/18-z)+12z=4/7$ so $z=29/630$.
5. Days for Z: $1/z=630/29$ which is $21.724...$, so about 22 days.

FINAL_ANSWER: b

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